Question

Which of the following statements use only exact numbers? (a) The temperature in our dorm room is kept at \(72^{\circ} \mathrm{F}\). (b) I bought 6 eggs, 2 cookies, and 5 tomatoes at the farmers' market. (c) There are \(1 \times 10^{9}\) nanometers in 1 meter.

Short answer

a) The temperature in our dorm room is kept at \(72^{\circ} \mathrm{F}\). b) I bought 6 eggs, 2 cookies, and 5 tomatoes at the farmers' market. c) There are \(1 \times 10^{9}\) nanometers in 1 meter. Answer: Statements (b) and (c) use only exact numbers.

Step-by-step solution

Statement (a)

The temperature in our dorm room is kept at \(72^{\circ} \mathrm{F}\). In this statement, the temperature is a measured value and may not be completely accurate or precise, as temperature measurement devices have some level of uncertainty. Hence, this statement does not use only exact numbers.

Statement (b)

I bought 6 eggs, 2 cookies, and 5 tomatoes at the farmers' market. In this statement, the numbers of the eggs, cookies, and tomatoes are counts of objects, which means they are exact numbers. Therefore, this statement uses only exact numbers.

Statement (c)

There are \(1 \times 10^{9}\) nanometers in 1 meter. In this statement, the number of nanometers is a defined conversion factor, which means it is an exact number representing the relation between nanometers and meters. Therefore, this statement uses only exact numbers. So, based on our analysis, statements (b) and (c) use only exact numbers.